Introducing a Disturbance into Logit and Probit Regression Models

Logit and probit regression models for dichotomous data make no explicit allowance for heterogeneity induced by omitted explanatory variables or by random fluctuations. This article considers several alternative models for incorporating heterogeneity by the inclusion of a disturbance term. When all the observations are independent, the presence of the disturbance has few empirical consequences. In particular, the variance of the observed counts does not increase and conventional estimators are still appropriate. For some models, however, the disturbance variance may invalidate cross-population comparisons. Quite different implications arise with grouped data when there is a single realization of the disturbance for each group. The observed variance is increased and conventional estimators are inefficient. Several alternative estimators are considered.